What wavelength lambda should the astrophysicist look for to detect a transition of an electron from the n= 6?

Question

An astrophysicist working at an observatory is interested in finding clouds of hydrogen in the galaxy. Usually hydrogen is detected by looking for the Balmer series of spectral lines in the visible spectrum. Unfortunately, the instrument that detects hydrogen emission spectra at this particular observatory is not working very well and only detects spectra in the infrared region of electromagnetic radiation. Therefore the astrophysicist decides to check for hydrogen by looking at the Paschen series, which produces spectral lines in the infrared part of the spectrum. The Paschen series describes the wavelengths of light emitted by the decay of electrons from higher orbits to the n=3 level.

Answer 1

You take the formula:

Energy = (h * c) / (lambda) where h is Planck's constant of 6.626 * 10^-34 J*s and c is the speed of light which is 3.00 * 10^8 m/s.

From this, you would use the Energy portion of the formula to be the energy lost between the transition of n=6 to n=3. To calculate the energy lost in transition, you would take the formula:

Energy lost = -2.18 * 10^-18 J * (1 / n^2) where n is the orbital you are going from (or in our case 6 which squared is 36).

Thus, once calculated the energy lost between the transition is found to be 1.814 * 10^-19.

Plugging this into the first formula, the wavelength would be found to be 1.09 * 10^-6 m.

PS: This also matches with the nanometers calculation found if you were to look in the Wikipedia article.



Hope this helps!

Answer 2

http://en.wikipedia.org/wiki/Paschen_series